Soft-sphere packings at finite pressure but unstable to shear

When are athermal soft-sphere packings jammed? Any experimentally relevant definition must, at the very least, require a jammed packing to resist shear. We demonstrate that widely used (numerical) protocols, in which particles are compressed together, can and do produce packings that are unstable to shear-and that the probability of generating such packings reaches one near jamming. We introduce a new protocol which, by allowing the system to explore different box shapes as it equilibrates, generates truly jammed packings with strictly positive shear moduli G. For these packings, the scaling of the average of G is consistent with earlier results, while the probability distribution P(G) exhibits novel and rich scalings.